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Exotic multiplications on Morava K-theories and their liftings. (English) Zbl 0729.55001
Théorie de l’homotopie, Colloq. CNRS-NSF-SMF, Luminy/Fr. 1988, Astérisque 191, 35-43 (1990).
[For the entire collection see Zbl 0721.00021.]
Let \(v_ n^{-1}BP\) denote the localization at \(v_ n\) of the Brown- Peterson spectrum associated to the odd prime p. Let \({\mathcal M}\triangleleft v_ n^{-1}BP_*\) be a maximal ideal containing the invariant prime ideal \(I_ n=(p,v_ 1,...,v_{n-1})\). \({\mathcal M}\) defines a ring spectrum K(\({\mathcal M})\). Now assume that K(\({\mathcal M})_*\cong K(n)_*\cong {\mathbb{F}}_ p[v_ n,v_ n^{-1}]\) and denote by \(v_ n^{-1}BP({\mathcal M})\) the Artinian completion of \(v_ n^{- 1}BP\) with respect to \({\mathcal M}\). The author constructs a splitting of \(v_ n^{-1}BP({\mathcal M})\) similar to that given in the paper reviewed below (see Zbl 0729.55002).
55N15 Topological \(K\)-theory